I thought that maybe I needed the killing animiation, where you stab a saber cat in the mouth or something to get it to work, but that made no difference. I've killed dragons, spiders, ranged takedowns on tons of enemies, out in the open world. I've killed the nord "undead" sorta guys(draugr?), skeletons and even things that have "grand" souls, had I trapped their souls.
This is supposed to recharge the weapon that you use to take down the enemy, correct? By at least a small amount. My axe I am using at the moment hasnt appeared to regain anything, been a normal glass axe for a while while I've been trying to get this perk to work, again.
Edit:Just noticed the Typo in the title. That should say Broken,

